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Categories (Aristotle)
Categories is the primary text of Aristotle's collective works on logic - labelled the Organon by Medieval scholars. Its set of doctrines is the backbone of Aristotelian philosophy and a source of commentary for some of the greatest philosophers of the last two thousand years, including Plotinus, Aquinas, Descartes, Locke, Kant, Hegel, Russell and Heidegger. The logical doctrines of this text collectively constitute Categorialism. Analysts often divide the Categories into three parts: Antepraedicamenta (ch. 1-4), Praedicamenta (ch. 5-9), and PostPraedicamenta (ch. 10-15), from the Latin word for categories. The first part briefly discusses homonyms, word composition and a fourfold division of semantic relationships. These ways in which words relate to each other are the guiding principles for the text's classification of things into categories, e.g. substance, quantity, position, etc. The latter parts discuss the categories themselves - enumerating and describing them - and then priority, motion, opposition, simultaneity, and having. Aristotle's virtue ethics and hylomorphic metaphysics are both grounded in categorialism. Therefore, the Categories is a reasonable starting point for people new to the Philosopher or, in general, to those who are new to studying philosophy. Background Knowledge The text's simplicity owes itself to the fundamental nature of its topics, which require scarce background knowledge, other than how to read, to understand. The most complex notion in the Categories is predication. To predicate one thing of another is to describe the former by means of the latter. Another way of putting it is that "X is predicated of y" is the same as "X is said of y", e.g. "An apple is a fruit" where "fruit" is used to describe "an apple" since an apple displays all the qualities of fruits. All other concepts are lucidly presented in the text. Naming Aristotle begins by identifying three semantic comparisons of names (nouns): *'homonyms' = different definitions used for the same word Homonyms are equivocally named, in that there are multiple definitions for different things named using that word - as when calling a compliment sweet and a candy sweet. *'synonyms' = same definition used for the same word Synonyms are univocally named, in that different things are named using one definition of that word - as when a rose and a tree are each called a plant. *'paronyms' = words that are derived from the same root word Paronyms are derivatively named from the same root. In general, the paronyms are modifications of the root in the manner of general and generic from the root genus or Canadian from Canada. These distinctions permeate the works of Aristotle, in particular his inquiry into the science of being'' qua'' being. As a further classification of language, Aristotle divides terms into simple and composite. Simply put, the simple terms consist of one word and the composite terms consist of multiple words. An example of the latter is "the fire burns" while examples of the former range from "zit" to "antidisestablishmentarianism". Fourfold Categorization Names can be classified in four ways: #what is predicable-of but not present-in anything #what is present-in but not predicable-of anything #what is both present-in and predicable-of something #what is neither predicable-of nor present-in anything That which is predicable of - i.e. said-of - a subject must be universal. Other names are particular. "Whiteness" can be predicated of Socrates but "Socrates' whiteness" can only be present in Socrates. Predicating "Socrates' whiteness" of the subject Socrates is nonsense, or else considers the name as universal. Distinguishing said-of from not said-of depends solely on whether a name refers respectively to what is universal or particular. That which is present-in a subject must be one of its accidental features, such as "Socrates' hand" is of Socrates. For a thing to be accidental to a subject is for it to stay essentially the same whether or not that thing is present. In the given case, Socrates does not cease to be Socrates if he loses a hand but does if he ceases to be a man (if it is essential that Socrates is human). Essential features of a subject are not present-in that subject. We must note that while "man" may not be present-in Socrates it is predicable of him and, therefore, universal. With both binary characteristics, Aristotle is able to present a fourfold division of names. In our examples, "man" is an essential universal; "whiteness" is an accidental universal; and "Socrates' whiteness" is an accidental particular. What then was the essential particular? Obviously the essential particular is "Socrates" himself, the subject to which the other names are related. Particulars & Universals The notions of particular and universal presented by the Categories merits analysis. "that which is individual and has the character of a unit is never predicable of a subject" (Categories 1b6) This summarizes Aristotles view of predication and particulars as they are - incompatible. A certain color cannot be said of an object. One cannot state that "Plato is Plato's white" but one can note that Plato has Plato's whiteness in himself and state that "Plato is white". Notice the universality and particularity of terms. The false belief that one can prove Aristotle wrong here may stem from a single kind of error, viz. failing to realize that every particular is a particular instance of a universal. "Blackness" is predicable of a crow and "a crow's black" is black, in that "black" is predicable of "a crow's black". One is mistaken when missing that "black" is to "a crow's black" what "man" is to "Socrates". Only the general names are predicable of a subject and even when the general name is included in the particular name, as in "subject's X", the particular is not predicable of anything. 'Accidental Particulars' The notion that one thing is present-in another may be confusing and has spawned recent academic debate from the likes of J. L. Ackrill and G. E. L. Owen, prominent classicist philosophers. Ackrill championed a traditional interpretation wherein, for example, "Caesar's white" and "John's white" are numerically distinct but qualitatively identical (i.e. perfectly resembling) units. Their identity is the perfect qualitative resemblance of each "white" and their distinction is in their presence in different bodies. Owen opposes the above notion that certain whites are tropes, i.e. unique instances/examples of a general thing, by denying that what is present-in but not predicable-of a thing can be an accidental particular. Accidental particulars are a mistaken idea in his view. Their debate hinges on the passage defining present-in. "B''y being ‘present in a subject’ I do not mean present as parts are present in a whole, but being incapable of existence apart from the said subject." (''Categories 1a23) The definition is somewhat ambiguous but two points are obvious. 'x is in y' = (a) x is not a part of y, and (b) x cannot exist separately from y Saying that x is not part of y exposes x's accidental quality, i.e. y does not need x. Scholars like Frede agree that for x not to be part of y is not to be in y's definition since Aristotle would contradict himself if he denied that x can physically be a part of y. For Aristotle, the accident x inheres in the subject y. Inherence is to be a property of or to belong to something. Hence, what is present in y inheres in y. Thus a necessary final addition to the definition is: © x belongs to y Ignoring this would deny x's existence since it has been established that x cannot exist apart from y. Ackrill and Owen's debate tackles a subtle difference. Namely, when we say 'Plato is white', does 'whiteness' or 'Plato's white' inhere in Plato? That is to say, is a universal or particular accidental present in Plato? The simple answer, according to Ackrill, is that only the particular is present in the subject. But what is present in a subject cannot exist apart from said subject and accidental universals can exist separately from any individual subject - e.g. whiteness can be found in Socrates, Hume, Reid and many other people than Plato. Thus no universal can be present in an individual subject. White would not be present in Plato, only Plato's white. But then what is meant by 'Plato is white'? Ackrill's interpretation seems contrary to how we speak. Owen supports this problem, suggesting the solution lies in reinterpretation of line 1a23 in accordance with another comment by Aristotle: "color is present in body, therefore in individual bodies, for if there were no individual body in which it was was present, it could not be present in body at all." (Categories 2b1-4) Here Owen believes the Philosopher speaks of universal color as present in a particular body. His modification of the definition swaps the second part with the following: (b')x cannot exist separately from some z An x that relies on some z to exist retains the dependence of the old definition. So white can be present in some people while being separable from Plato - a specific y. Under the new definition, Plato shares the white that is in Hume as long as they are qualitatively the same color, i.e. not if each man's color differs like a leaf's green from a tree's brown.'' In short, Owen claims accidental particulars don't exist and only universals inhere in a subject. Neither interpretation clearly matches the text since Ackrill assumes Aristotle mispoke in the passage from 1b and Owen thinks Aristotle means to say a universal when talking of a 'certain whiteness'. Yet their complaints against each other's positions are valid. Unfortunately, they have validity because neither side is totally supported by the way people naturally speak. Asking whether 'Aristotle's white on Tuesday' is the same as 'Aristotle's white on Friday' proposes a unique question of identity - one probably not considered by the Philosopher - hence, worth ignoring here. 'Genera & Differentiae' When predicating a universal of something, everything that is predicable of the predicate is predicable of the subject. The ''Mona Lisa, for example, is a painting and paintings are art, therefore the Mona Lisa is art. Less general predicates are the species of a genus, the more general predicate. A species' differentia sets it apart from other species in its genus, as grammatical knowledge is distinct from scientific knowledge by being 'grammatical'. Differentiae are the criteria for distinguishing any one species within a single genus. The differentiae of two different genera aren't usually comparable. This is quite obvious when comparing the differentiae of plants and animals. 'Covered in bark' and 'leafed' are not how we distinguish species of animals any more than 'two-footed' or 'winged' distinguish species of plants. However, incommensurability of some differentiae is a warning not a necessary rule. We easily prove this by looking at how plants and animals can be classed into 'poisonous' and 'non-poisonous' species. A nearly infinite number of examples can make the case. The cautionary point here is ignored when making a category mistake. Illustrating such an error is as easy as providing examples earler. Consider 'Some men are agnostic', a perfectly normal statement since men can, in principle, be agnostic. Then think that 'Some pineapples are agnostic' to make a category mistake since it is not possible for something that cannot have an opinion, like a pineapple, to be agnostic. Praedicamenta The Categories heart and soul is the explicit enumeration of all 10 categories that follows their implicit exposition in the Pre-Predicamenta - a tenfold system from a fourfold principle. A category is one of the highest kinds into which names can be classed. Highest implies that a category cannot be called a kind of X whereas every genus or particular is a kind of a category. Supremacy of categories is categorialism's first principle. 'The Ten Categories' *'Substance' (ousia): Divides into two classes - primary substance and secondary substance. The latter is a universal that is predicable of particular things, the former is the particular entity that can neither be predicated-of nor present-in another thing. *'Quantity' (poson): Divides into two classes - continuous quantities and discrete quantities. This is also split into two classes - ordered quantities and unordered quantities. Whether quantities or quantified things fall under this category, however, is not clear in the text. *'Relatives' (pros ti): This is the reciprocal classification of things, how they may be related to one another. *'Quality' (poion): Divides into four classes - dispositions, natural capacities, affections and shapes. These are the kinds of differentia. Within Quality, as the highest kind, there is no differentia to distinguish each of its classes. This might be because its species are the criteria presupposed for all differentiae/distinctions. The rest are enumerated briefly in the Categories and admit of examples as well as summaries: *'Place' (pou): Spatial position relative to physical surroundings, e.g. 'in New York' or 'at his house'. *'Time' (pote): Temporal position relative to either a universal scheme of measuring time or to the present, e.g. '1781' or 'yesterday' respectively. *'Posture' (keisthai): Relation of an object's parts in a state of rest or, some argue, the state of rest itself, e.g. 'sitting' or 'stretching'. *'Having' (echein): State or condition of possessing something, e.g. 'armed' or 'clothed'. Posture and having are hard to consider separately from quality without some arbitrary difference. *'Affection '(poiein): Reception of change from another object. Affection is demonstrated in language by the passive voice, e.g. 'to be written', 'to be stabbed' or 'to get what's coming to you'. *'Action' (paschein): Production of change in another object. Contrary to affection, action is demonstrated by the active voice, e.g. 'to write', 'to harm' or 'to arrest'. The symmetry and generality of Aristotle's two classifying schemes lends them a certain beauty yet philosophers have found numerous ways to improve on the categories. For an early work in philosophy, however, Aristotle's categorialism is an impressive system. 'Substance' Substance is understood by Aristotle in two senses. The "truest and primary and most definite sense of the word" (Categories 2a11) is the essential particular discussed earlier - that which is neither predicable of nor present in anything. As the only category with this distinction, primary substances are what every other thing is ultimately predicated-of and present-in. This is unique and fundamental to all primary substances. The secondary sense of the word is the essential universal - that which is predicable-of but not present-in things. Species and genera are the secondary substances of categorialism. Thus the species 'man' and genus 'animal' are secondary substances predicated of Socrates, a primary substance. For illustration, Socrates can be viewed as a primary substance of which many secondary ones are predicable: *'Socrates' (primary substance) **'Man', 'Socrates is a man' ***'Animal', 'Men are animals', 'Socrates is an animal' ****'Living Being' 'Animals are living', 'Men are living', &c *****'Extend Being' 'Living beings are extended', &c ******'Substance' 'Extended beings are substances', &c Our illustration shows two things: substance is a highest kind as Aristotle argues and what is predicable of an individual or a species is also predicable of their genera. So 'animal' is predicable of 'man' and of 'Socrates' under an identical definition of 'animal'. Ironically, the genus 'primary substances' is a secondary substance, that is predicable of all primary substances. Keeping this in mind can avoid some confusion. Aristotle identifies three marks of substance. First, one not unique to it, is that a substance does not admit of a contrary, in the sense that nothing is opposite to man or bipedal except not-man and not-two-footed. Second, while one substance may be more or less substantial than another - as primaries are to secondaries - there is no variation of degree within a substance. This can be verified by almost infinite examples, like that Jean-Paul is no less a man than Albert, and neither are less animals than Paul the Octopus. Third, a substance has the unique ability to retain numerical unity, i.e. still be itself, and display contrary qualities. Since other marks of a substance are sometimes found in other kinds, persistence over changes in its properties is the most distinctive mark of what is a substance. 'Quantity' Quantity admits of division in two ways: *''discrete quantities and ''continuous quantities - by how a certain quantity is divisible *''ordered quantities'' and unordered quantities - by whether or not a quantity's parts stand in relation A quantity is discrete when there is "no common boundary among the parts" (Categories 4b30). This is to say there is broken progression of the quantity. Speech is a fine example of this as it is distinguished into discrete syllables that, even under slurring of words, have no boundaries between each other. The integers are also discrete (1, 2, 3, 4, &c), as 4 and 5 are not joined in any sense nor are other whole numbers. Continuous quantities are more controversial in modern philosophy but seemed obvious to Aristotle. Geometrical figures like lines, planes and solids are continuous. The shared boundary of two parts of a line is a mathematical point, that of a planar figure's parts is a line and two parts of a solid share a surface. Real numbers are continuous as well. These arguments can be proven by taking the limit of a function like y = x at any point along a closed interval b and finding that the limit exists and is equal to the function over the entire interval. However, continuity is controversial when applied to Time and Space. Aristotle says that they are continuous but philosophers from Zeno to Hume and Kant argue that this is impossible or that the truth of such a claim is unknowable. But these problems have little bearing on continuity per se. Of ordered quantities, some are related in position. In fact, position is Aristotle's only distinction for related parts, as he considered all quantities to be in some sense ordered. Length, surface, body and space are listed as positional quantities while all variety of number, time and speech are merely ordered by some manner of successive parts. His criterion is obvious, viz. the relation between parts of positioned quantities can be visualized simultaneously whereas a part of a quantity like time is fleeting as it gives way to the next part. One can certainly imagine a series of numbers in relative positions but only by taking them as parts of a surface. General categorization of quantities might look like: *'Continuous Quantities' (ordered) **''Simultaneous'' (Positional) ***Line ***Surface ***Body ***Space **''Successive'' (Non-positional) ***Time ***Real Number *'Discrete Quantities' **''Ordered'' ***Integer ***Speech ***Sequence ***Series **''Unordered'' ***Set Aristotle did not include many of the above in his enumeration of quantities, likely since he had no notion, as far as we know, of sets, sequences and series, or of numbers as real, &c. But it is only reasonable to include them in a comprehensive modern list of quantities. However, one difficulty is apparent when reclassing quantitative kinds. Modern interpretations of the Categories fail to see whether Aristotle intended to divide quantity into quantities or quantified things. The latter differs from the former by being an instance or example of an amount. There's no simple answer but it bears reminding that Aristotle intended Quantity to be a highest kind. Thus a quantity cannot be an instance of some other kind like substance or relation; it is solely quantitative. The answer this interpretation illuminates is that quantities are amounts strictly speaking. A bushel, for example, is nothing other than quantity. Bushels are predicable of primary substances (e.g. apples), do not admit of a definite contrary, and cannot be a differentia of any genus. By extension, a 'bushel of apples' is a quantity insofar as it is a bushel and is a substance as it comprises individual apples. The aspect of being a set of something makes it a quantity, but it derives this nature from bushel's status as quantity so it is a secondary quantity. 'Four' is a quantity for similar reasons as a subset of the series of natural numbers; likewise, 'four horses' is a secondary quantity that consists of primary substances. Postpraedicamenta References *E. M. Edghill, trans, Categories of Aristotle ''(New York: Random House, inc, 1941) *G.E.L. Owen, "Particular and General." ''Proceeding of the Aristotelian Society (1978) 79: 1-21 *J.L. Ackrill, Aristotle: Categories and De Interpretatione, (Oxford: Clarendon Press, 1963) *James Duerlinger, "Predication and Inherence in Aristotle's Categories", Phronesis, (1970), Accessed at: http://www.jstor.org/stable/4181850?seq=1 Category:Works (Aristotle)